Unary Inequalities Group Practice Problems Do not apply problems

"The Application of Unary Inequality Group" is a micro-course provided by Meichonghu Middle School in Changfeng County, and the main teacher is Chen Cheng.

Combined with the learning of the knowledge of unary inequality groups, students can list and solve inequality groups according to the quantitative relationships in practical problems, so as to improve students' ability to analyze problems.

Basic steps to apply inequalities to solve real-world problems:

1.Carefully examine the problem, analyze the relationship between known quantities, unknown quantities and unequal quantities, and briefly express them in a textual style;

2.Appropriate unknowns are set according to the needs of the problem, and the relevant quantities are expressed in algebraic formulas containing unknowns.

3.Replace expressions expressed in words with algebraic expressions and inequality symbols, and list inequalities according to inequality relations;

4.Find the solution set of the inequality, check whether the solution set is in line with the question, and write the answer.

The first. There are x dormitories, which can be listed in the following two types.

4x+20＞8x

4x+20＜8x+8

The two-formula solution can be obtained.

5 x 3 x = 4 because x is an integer

That is, the number of students in the dormitory is 4 times 4 + 20 = 36 people.

Question 2. If there are x vacant rooms on the first floor, then there are x+5 vacant rooms on the second floor.

5x＞484x＜48

4(x+5)＞48

3(x+5)＜48

Combining the above solutions, we can get, 11 x

Therefore, x=10

There are 10 vacant rooms on the first floor and 15 vacant rooms on the second floor.

I hope my answer is helpful to you.

For the eighth-grade spring outing, if you rent a number of 48-seat buses, they will be full; If you rent a 64-seater bus, you can rent one less bus, and there is one that is not full but more than half. It is known that the cost of renting a 48-seater bus is 250 yuan, and the cost of renting a 64-seat bus is 300 yuan. So what kind of bus should you rent more cost-effectively?

Equipped with x cars.

The total number of people is 48x

Then according to the title.

48x-（x-2）*64>32

48x-(x-2)*64<64

128-16x>32

128-16x<64

An integer when 4x is solved.

So x=5, then the cost of renting 48 bits is 5 * 250 = 125064 bit of the cost of 4 * 300 = 1200

It is clear that the comparative accounting of renting 64 bits.

There are 5 fewer rooms on the first floor of a hotel than on the second floor, and there are 48 people in a tour group, if all are arranged on the first floor, 4 people per room, the room is not enough, 5 people per room, and the room is not full; If you arrange to live on the second floor, each room for 3 people is not enough, 4 people per room, there are rooms that are not full, ask how many rooms are there on the first floor of the hotel?

Solution: There are x rooms on the first floor, then there are x+5 rooms on the second floor, there are 4x<48,,, solution gets x<12, and from 5x>48,,, solution gets x>. And because, 3(x+5)<48,,, solution gives x<11,,4(x+5)>48,,, solves x>7...

To sum up, yes

3x(x+5)＞3x2+7

x-4 < 2x+1

3x+14 > 4(2x-9)

3x-7≥4x-4

2x-3x-3＜6

x-4 < 2x+1

2x-6 < x-2

3×10x<500

7（x+3）>98

2x-3x+3＜6

2x-3x+1＜6

2x-3x+3＜1

2x-19＜7x+31

3x-2(9-x)＞3(7+2x)-(11-6x)2(3x-1)-3(4x+5)≤x-4(x-7)2(x-1)-x＞3(x-1)-3x-5

15-(7+5x)≤2x+(5-3x)

2x+3＞0

3x+5＞0

5x+6＜3x

4（2x-3）＞5（x+2）

2x+4＜0

5x-2≥3（x+1）

2（x-3）≤4

5m-3>0

2x-3(x-1) >6

6x-3(x-1) ≤12-2(x+2)

3(1-3x) <4(x-1)

8-7x+1 > 2(3x-2)

3x+14 > 4(2x-9)

3-3m<-2m

5x+3x＞2

3y+9＜7

3+8)x＞6

5-3/1 x＞5

11x-5x＞3

3a-9a＞11

4a+9＞6

33x+33＜1

5b-9＜9b

6x+8＞3x+8

3x-7≥4x-42x-19＜7x+31．3x-2(9-x)＞3(7+2x)-(11-6x)．2(3x-1)-3(4x+5)≤x-4(x-7)．2(x-1)-x＞3(x-1)-3x-5．3[y-2(y-7)]≤4y．

15-(7+5x)≤2x+(5-3x)．

3*10x<500

3*10(x+1)>500

7（x+3）>98

7x<98

I don't know if you need an answer, so I didn't type the answer.

1 Write the solution set of the following inequality:

2x 14 0 1 2x 45 5x 3x 2 Solve the unary one-time inequality: 4(x 3) 2(x 1).

3．(y＋1)／3＋1＜(y－1)／2＋(2y－1)／6。

4．3[x－2(x－2)]＞x－3(x－3)。

5 Find the positive integer solution of inequality (x 1) 2 (x 1) 3 (1 x) 6.

Individualized exercise design.

1 Knowing the equation about x (x m) 3 (2x 1) The solution of 2 m is a positive number, find the range of values of m.

2 If the difference between the algebraic equation (3y 14) and (9y 2) 7 is greater than 6 and less than 8, find the value of y.